# Spin currents, spin torques, and the concept of spin superfluidity

## TL;DR

This paper clarifies the distinction between different types of spin currents in non-collinear magnets, emphasizing that translational spin transport is polarized along local magnetization and cannot occur at zero temperature in insulators, impacting the understanding of spin supercurrents.

## Contribution

It provides a method to separate translational and precessional spin transport and clarifies the conditions under which spin supercurrents can exist in magnetic insulators.

## Key findings

- Translational spin movement aligns with local magnetization.
- At zero temperature, insulators cannot support translational spin currents.
- The interpretation of spin supercurrents is affected by these distinctions.

## Abstract

In magnets with non-collinear spin configuration the expectation value of the conventionally defined spin current operator contains a contribution which renormalizes an external magnetic field and hence affects only the precessional motion of the spin polarization. This term, which has been named angular spin current by Sun and Xie [Phys. Rev B 72, 245305 (2005)], does not describe the translational motion of magnetic moments. We give a prescription how to separate these two types of spin transport and show that the translational movement of the spin is always polarized along the direction of the local magnetization. We also show that at vanishing temperature the classical magnetic order parameter in magnetic insulators cannot carry a translational spin current, and elucidate how this affects the interpretation of spin supercurrents.